Some Properties of Grey S-Acts Over Monoids

Masoomeh Hezarjaribi and Zohreh Habibi ()
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Masoomeh Hezarjaribi: Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, Iran
Zohreh Habibi: Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, Iran

New Mathematics and Natural Computation (NMNC), 2022, vol. 18, issue 02, 313-323

Abstract: In this paper, we introduce the concept of grey S-acts and morphisms between grey S-acts on monoids, which construct a category, namely, Act0 − GS. Next, we define indecomposable, cyclic, free and projective grey S-acts. We show that any grey S-act is a free grey S-act if and only if it is a free object in this category. Also, we show that any grey S-act is epimorphism image of any free grey S-act. We prove that any free grey S-act is a projective grey S-act and any cyclic grey S-act is an indecomposable grey S-act.

Keywords: Cyclic; free; grey S-act; indecomposable; monoid; projective (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S1793005722500168

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